The invention relates to electrostatic Kingdon ion traps in which ions can oscillate harmonically in the longitudinal direction, decoupled from their motions in the transverse direction. Kingdon ion traps are electrostatic ion traps in which ions can orbit around one or more inner longitudinal electrodes or oscillate in the center plane between inner longitudinal electrodes, while an outer, enclosing housing is at a DC potential which the ions with a specified kinetic energy cannot reach. A very simple Kingdon ion trap consists of a rod (in the ideal case, an infinitely long rod) as the inner electrode and a surrounding tube as the housing or outer electrode (FIG. 1). In special Kingdon ion traps which are particularly suitable for mass spectrometers, the inner surfaces of the housing electrodes and the outer surfaces of the inner electrodes are shaped so that, firstly, the motions of the ions in the longitudinal direction (z) of the Kingdon ion trap are decoupled from their motions in the transverse direction (x, y) or (r, φ) and, secondly, a parabolic potential profile is generated in the longitudinal direction in which the ions can oscillate harmonically.
In this document, the term “Kingdon ion traps” refers only to these special forms in which ions can oscillate harmonically in the longitudinal direction, decoupled from their motions in the transverse direction.
The document U.S. Pat. No. 5,886,346 (A. A. Makarov) elucidates the fundamentals of a special Kingdon ion trap which was introduced by Thermo-Fischer Scientific GmbH Bremen under the name Orbitrap®. This ion trap consists of a housing electrode which is split across the center and a single spindle-shaped coaxial inner electrode (FIGS. 2 and 3). The housing electrode has an ion-repelling electric potential and the inner electrode an ion-attracting electric potential. With the aid of a special ion-optical device and a special injection method, the ions are tangentially injected through an opening in the housing electrode and then orbit in the hyperlogarithmic electric potential of the ion trap. The kinetic injection energy of the ions is set so that the attractive forces and the centrifugal forces are in balance, and the ions therefore largely move on virtually circular trajectories.
The cross-sections of the inner surface of the housing electrodes and the outer surfaces of the inner electrodes are both circular. The hyperlogarithmic potential between inner and outer electrodes is represented byΨOrbitrap(r, φ, z)=Ψ1z2/l12−Ψ1r2/2l12+2Ψ2ln(r/l2)+Ψ3.
In the document U.S. Pat. No. 7,994,473 B2 (C. Köster; correspondent to DE 10 2007 024 858 B4 and GB 2448413 B), which is incorporated herein by reference, other types of Kingdon ion trap are described which, in their basic form, have precisely two inner electrodes (FIG. 4). In this case, as well, the inner electrodes and the outer housing electrodes can be precisely shaped in such a way that a potential distribution is formed in which the longitudinal motions are decoupled from the transverse motions, and a parabolic potential well is created in the longitudinal direction to generate a harmonic oscillation. The potential of this “bipolar Cassini ion trap” is represented in a general form byΨ(r, φ, z)=Ψ1z2/l12−Ψ1{r2(1−k)sin2φ+kcos2φ)/l12}+Ψ2ln{(r4−2b2r2cos(2φ)+b4)/l24}+Ψ3.With this potential distribution, the exact inner shapes of the housing electrodes and the outer shapes of the inner electrodes are described by two fixed values for Ψ(r,φ, z)=ΨOuter and Ψ(r, φ, z)=ΨInner because each of these must form equipotential surfaces of the desired field. These “bipolar Cassini ion traps” or “second-order Cassini ion traps” are characterized by the fact that the ions not only fly on complicated trajectories around the two inner electrodes, but can also oscillate in the center plane between the two inner electrodes. The ions orbiting around or oscillating between the electrodes in this way can then execute harmonic oscillations in the longitudinal direction.
Bipolar Cassini curves are curves in a plane, which can be defined like plane ellipses. While an ellipse is the quantity of all points whose distances al and a2 from two focal points result in a constant sum s (a1+a2=s), a Cassini curve is the quantity of all points whose distances al and a2 from two focal points (called “poles” here) result in a constant product p:a1×a2=p. In the same way as ellipses degenerate to circles if the two foci coincide to form one focus, Cassini curves also degenerate to circles if the two poles coincide to form one pole. Ellipses form a concentric family of curves with s as the family parameter. As shown in FIG. 6, Cassini curves form a family of curves which form ellipse-like curves around the two poles for large values of p; if p becomes smaller, the curves begin to constrict. With even smaller p, a lemniscate is formed, and for even smaller values of p the Cassini curve splits into two closed curves which each surround one pole. The cross-section of the housing of the bipolar Cassini ion trap is described by a large value of p, the cross-section of the two inner electrodes by a small value for p.
The term Ψ2ln{(r4−2b2r2 cos(2φ)+b4)/ l24} contains, in the curly brackets, the equation for a family of Cassini curves; the term Ψ1z2/l2 represents the axial potential well, which is independent of r and φ. The term Ψ1{r2(1−k)sin2φ+k cos2φ)/l12}, which modifies the radial potential distribution, is included so that the Laplace condition ∇2Ψ=0 is fulfilled, which must apply to all potential distributions.
By superimposing the potentials of several bipolar Cassini ion traps with suitable twists and shifts, it is possible to design ion traps with three, four and more inner electrodes, as is stated in the document U.S. Pat. No. 7,994,473 B2. These still belong to the class of second-order Cassini ion traps, however.
In contrast to ellipses, the Cassini curves can be expanded to n-polar curves. These curves are the quantities of all points in a plane whose distances ai(i=1 . . . n) from the n poles result in constant products p:Πi=1i=n(ai)=p . These n-polar Cassini curves are also called Cassini curves of the nth order. These also include curves which surround all poles together, as well as n curves which each surround one pole. FIGS. 5, 6 and 7 illustrate families of Cassini curves of the first, second and third order.
In view of the above there is a need to find further electrostatic ion traps in which ions can oscillate harmonically in the longitudinal direction, decoupled from their motions in the transverse direction.